The Canaries signed off from what has been an impressive return to the Barclays Premier League with a 2-0 victory over Aston Villa at Carrow Road, which secured 12th place.
Lambert has masterminded successive promotions since taking over in August 2009 when the Norfolk club were languishing in the lower reaches of npower League One and facing an uncertain future.
However, it is the 42-year-old's achievements this season with an industrious side packed full of hardworking, unheralded names which have seen the former Celtic midfielder linked with a move away from East Anglia should a suitable vacancy occur.
Indeed, the Villa fans yesterday [Sunday] chanted Lambert's name and called for the dismissal of manager Alex McLeish, and they got their wish today [Monday] when the Scot was sacked following a disappointing campaign.
Lambert agreed a new deal in May 2011, along with his backroom staff, and chief executive McNally insists the highly-rated Scot is going nowhere.
"We would not welcome any enquiry for our football manager or any of the club's football players," McNally told BBC Radio Norfolk.
"We will do everything we can and fight this as hard as we have ever fought."
McNally added: "If I was at another football club and I was looking for another manager he'd be top of my list.
"In any business you need to look at what might happen - the what ifs.
"But we are focused on keeping our manager and the footballers he wants to retain at the club and to bring in better footballers to complement the club.
"I want other clubs to covet our manager and to want our players, because if they do that means we're doing something right.
"It is almost obvious, isn't it, that clubs would like to have them at their football club."
Lambert accepts whatever happens in the future, Norwich's rise up through the league has been way ahead of schedule.
"It has been unbelievable what has happened here in three seasons - it is never easy to get one year of success, let alone three," he said.
"Every year has been a challenge since I have been here - getting out of League One was with how far we were behind the top two, then there was a challenge to stay in the Championship, let alone get out of it because of everything which had gone wrong, the club was at its lowest ebb.
"To do what they have done in three years has been too quick to do it, but we did and have been brilliant.
"You are always playing catch up because of what has happened - the chairman said we would have to stay in the Premier League again for another year before things start to build.
"Nobody expected this within three years. The club gave itself seven years to get in the Premier League, and that was allowing to be relegated again, so the rise has been huge."
Should Lambert remain in charge for pre-season planning, he accepts there will not be a deep transfer kitty with which to strengthen the squad.
"We can't go out and put the club it was in the position of financial trouble it was in two years ago," he said.
"As long as people realise we won't be able to do that, but that is my job, to try to get people in to try to complement things, the right type of player to try to help the team at the minute."